Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{5\pi i / 12}) \cdot ( e^{19\pi i / 12})$ (Your current answer will be plotted in orange.)
Solution: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{5\pi i / 12}$ ) has angle $\frac{5}{12}\pi$ and radius $2$ The second number ( $ e^{19\pi i / 12}$ ) has angle $\frac{19}{12}\pi$ and radius $1$ The radius of the result will be $2 \cdot 1$ , which is $2$ The angle of the result is $\frac{5}{12}\pi + \frac{19}{12}\pi = 0$ The radius of the result is $2$ and the angle of the result is $0$.